Let's solve the problem step-by-step to find Thandi's current age.
1. Define the variables:
- Let [tex]\( S \)[/tex] represent Sophie's current age.
- Let [tex]\( T \)[/tex] represent Thandi's current age.
2. Set up the equations based on the problem statements:
- We know from the problem that Thandi is six years older than Sophie. Therefore, we can write:
[tex]\[
T = S + 6
\][/tex]
- The second piece of information is that in three years, Thandi will be twice as old as Sophie. This can be translated into the following equation:
[tex]\[
T + 3 = 2 \times (S + 3)
\][/tex]
3. Substitute the first equation into the second equation:
Since [tex]\( T = S + 6 \)[/tex], we substitute [tex]\( T \)[/tex] in the second equation:
[tex]\[
(S + 6) + 3 = 2 \times (S + 3)
\][/tex]
4. Simplify the equation:
[tex]\[
S + 6 + 3 = 2S + 3 \times 2
\][/tex]
[tex]\[
S + 9 = 2S + 6
\][/tex]
5. Solve for [tex]\( S \)[/tex]:
To isolate [tex]\( S \)[/tex], we bring all terms involving [tex]\( S \)[/tex] to one side of the equation and constant terms to the other side:
[tex]\[
S + 9 - 6 = 2S
\][/tex]
[tex]\[
9 - 6 = 2S - S
\][/tex]
[tex]\[
3 = S
\][/tex]
Therefore, Sophie's current age is [tex]\( S = 3 \)[/tex] years.
6. Find Thandi's current age using the first equation:
[tex]\[
T = S + 6
\][/tex]
[tex]\[
T = 3 + 6
\][/tex]
[tex]\[
T = 9
\][/tex]
Thus, Thandi is currently 9 years old.
